Shift-Share Instruments: Review, Modification & Application
Using an empirical setting to estimate the causal effect of interprovincial services trade on interprovincial services trade on interprovincial goods trade in Canada, we demonstrate how applied researchers can develop, select and validate Shift-Share Instrumental Variables [SSIVs] in their studies. Leveraging a trade dataset for the years 2007 to 2019, we design a novel SSIV Search Method to construct 58 SSIVs, incorporating both established techniques and innovative modifications to address endogeneity in interprovincial analysis. Employing the Poisson Pseudo Maximum Likelihood [PPML] estimator within the gravity model, we find a significant causal effect of interprovincial services trade on interprovincial goods trade across just-identified [JI] and over-identified [OI] IV models. The results reveal that our SSIV variants, particularly those with lagged disaggregate shocks and shares, consistently outperform literature-suggested SSIVs in terms of empirical validity, predictive accuracy, and bias reduction. Evidence from Machine Learning techniques, such as Gradient Boosting and Random Forest models, suggests that our instruments have higher predictive power than literature-suggested instruments. Monte Carlo simulations further validate the low-bias properties of all SSIVs tested, with our variants consistently exhibiting lower bias. Notably, lagged disaggregate shocks and shares enhance the reliability of estimates by capturing regional and sectoral heterogeneity and eliminating potential contemporaneous correlations between the instruments and the outcome variable. Based on our experiment, we recommend using lagged disaggregate shocks and shares to construct SSIVs for the most reliable estimates. Indeed, we prepare a practical prescription for applied researchers to address and solve the endogeneity problem in interprovincial and similar empirical applications.
Trade and Migration: Evidence from SSIVs and Machine Learning
This paper examines the bi-directional causality between interprovincial trade (in aggregate and dis-aggregate) and migration within Canada for the years 2007 to 2019. Employing the PPML (Poisson Pseudo Maximum Likelihood) estimator in the gravity model framework, this study finds that both interprovincial trade (in aggregate and dis-aggregate) and migration significantly impact each other within Canada at a 1% significance level. To address the endogeneity problem between interprovincial trade and migration, we utilize the novel shift-share instrumental variable (SSIV) technique to develop 80 SSIVs for interprovincial trade (in aggregate and dis-aggregate) and 4 SSIVs for interprovincial migration. While deriving conventional SSIVs, we design our SSIVs with different combinations of aggregate and disaggregate shocks and shares without and with lags. The results reveal that all the SSIVs consistently demonstrate strong first-stage relevance with higher F-statistic and R-squared values. We find our estimations are robust across both just-identified and over-identified settings. We argue that our designed SSIVs with lag dis-aggregate shocks and shares address regional and industrial heterogeneity compared to the conventional SSIVs with aggregate shocks and eliminate any potential contemporaneous correlation between instruments and the endogenous variable. Our results also reveal that the influence of trade on migration is substantial compared to the impact of migration on trade. Notably, the services trade has a much stronger effect on attracting migrants than the goods trade. While migrants significantly influence both goods and services trade, this effect is slightly stronger on goods trade. Based on the findings, this study recommends provinces aiming to attract migrants should reduce overall trade barriers, especially services trade.
Endogeneity Between Trade & Migration:
Insights from Shift-Share Instruments & Machine Learning
This study explores the interplay between trade and migration within and across Canadian borders. Employing the Poisson Pseudo Maximum Likelihood [PPML] estimator in the gravity model for the years 2007 to 2019, we show how interprovincial trade and international trade influence interprovincial and international migration in Canada. To address the endogeneity problem between trade and migration, we derive 16 Shift-Share Instrumental Variables [SSIVs]
by following the construction method of Bartik instruments. This research compares the empirical performance of SSIVs in just-identified [JI] and over-identified [OI] IV models. The results indicate that all the instruments for trade are very strong and robust across all versions of IV models. Notably, the empirical performance of the modified SSIVs is better than that of the usual SSIVs. We also find that the empirical performance of SSIVs in OI IV models is better than that of JI IV models. While showing new ways to derive instruments, we examine the predictive strength of all these instruments utilizing a Machine Learning technique, the Random Forests [RF] model, for the first time in this literature. The findings reveal that the SSIVs and the shock instruments derived from exports have higher predictive strength than all other SSIVs. Especially, the impact of interprovincial trade on interprovincial migration is higher than the impact of international trade on international migration to Canada. Therefore, this paper suggests that the provinces keen on attracting migrants should minimize the trade barriers overall to encourage migrants interprovincially and internationally.
Machine Learning Shift-Share Instruments.
Exploring the Dynamics of Goods and Services Exporting Firms: Productivity, Sales, & the Role of Bi-Exporters.
Machine Learning Forecasting Models: ChatGPT vs Gemini.
First-Stage Caution With IVPPML.
Provincial and International Labor Mobility and Labor Market Conditions.
The Nexus Between R&D Expenditure and Migration.